Sugiyama never hated anyone, you're just repeating bullshit things that were spread by Twitter/Resetera and western journos. The guy was a japanese patriot and he was actually pretty chill about people's sexuality but quite rightfully so said people should keep that info in the bedroom.
The smear campaign against Sugiyama started around DQ9, but it took a more aggressive turn after DQ11 released in the West in 2018, in an attempt to have Square-Enix cut any ties with him (Squeenix only bothered with a PR statement). The "controversial" exchange with a politician during his channel show in 2015 re-surfaced again during the Tokyo Olympics too, once again to attempt to have him be cancelled.
東京オリンピック(五輪)開会式に『ドラゴンクエスト』のメーンテーマは本当に流れるのか――。 そんな話題が22日深夜、立憲民主党など野党関係者内にざわめきのよ...
biz-journal.jp
Basically, what Sugiyama re-affirmed that homos can't indeed reproduce (which is the main reason why the japanese politician Sugita believes it's a waste of tax money to support lgbtq in the long-term), admitting that japanese women are amazing, and that he's glad both men and women are able to voice their personal concerns. But I believe western faggots got mad he invited a "bigoted" politician into his show thus smeared him into a hateful caricature through social media and journalism.